Why Did San Francisco Schools Stop Teaching Algebra in Middle School?
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As a side note, I don't remember being taught algebra before the 9th grade either, in an excellent school district, and I was in a gifted class. I still kept my algebra textbook from the 10th grade and it's pretty standard algebra. In fact, I didn't even learn Calculus until college and I wasn't negatively impacted by that at all. However, this was almost 30 years ago so I'm sure educational standards have increased, but it's funny that what I learned back then is no longer "good enough".
I did not major in CS so I've never taken a formal Calc class. If anyone has a good recommendation for a MOOC or similar for a working professional to learn Calculus I'd love to take it. Doesn't need to be free, would probably be more motivated to do well if it wasn't :)
Paul's notes (http://tutorial.math.lamar.edu/) is apparently a really good reference too.
In the US, the term used is "Gifted & Talented" (abbreviated to "GT"). So, you frequently see courses or tracks labelled "gifted", "GT", etc.
At the high-school level, the label frequently changes to "honors" or "advanced". And you will also see Advanced Placement (AP) and International Baccalaureate (IB) which are brand names for honors/advanced curriculums that often offer college credit with high marks on exams.
That being said, I would never dream of sending my kid to public school regardless. Speaking of splitting kids up, I was placed into the "trouble" kids group (probably due to dyslexia or apathy) until I was eventually identified as "gifted" 6-7 years later[1]... I seriously think I have a slight bit of PTSD dealing with the screaming in a classroom all those years.
Mixing students is probably a hell of a lot worse than not. Then again S.F. is all about being "equal" to the point of insanity.
On the subject of mixing, I think mixing students is probably better overall. The "trouble" group is the result of splitting them out. You don't end up with a whole room of problematic kids and a couple of misidentified gifted kids when they are mixed. The only way it makes sense to split out the problematic kids is if they get a lower student:teacher ratio. They need more attention.
Probably not AP, so the college wouldn't accept it, right? That's the rub, really. Though to be honest my HS calculus was more like an intro with College being much more complex.
It depends on the specific kind of "trouble". If you have students who don't get the material, and need extra assistance, that's one thing. At least they don't "disrupt the learning environment" (as they say the edu-speak that teachers and administrators use).
On the other hand, if they are bored, really don't want to be there, blurt out things at random, make animal sounds to amuse themselves, etc., this affects other students and the whole mood of the classroom. (To say nothing of threats, hostile behavior, actual violence, etc.) Such students need to be physically removed in order to enable the others to learn undisrupted.
They also have reversed the classes and it works wonderfully for my kids. Every night, they are assigned a video to watch (something very similar in nature to Khan Academy videos) and the next day they work through problems in class. It works well for my kids because they learn by doing and so it seems that spending classroom time on that part makes sense.
So tragedy of the commons says I want my, top performing, kid to be in a gifted only class to maximize his potential. But as a society I want all kids grouped, as bringing up the average knowledge of the country is a very good goal (and important when you realize things such as everyone gets 1 vote, no matter intelligence).
Teaching on the other hand is a relatively high status, low risk profession.
It can be, for teachers in comfortable suburban schools where the students are generally well behaved.
For teachers in dangerous, urban schools with severe disciplinary and even criminal issues (gangs, violence, drugs, etc), it is not so low-risk.
No. 9: Police and sheriff's patrol officers Fatalities per 100k: 18.0
No. 7: Refuse and recyclable material collectors Fatalities per 100k: 22.8
Feel free to look for statistics though.
Both spend a lot of time standing on the side of the road but far fewer people will perform absurd traffic maneuvers to pass a cop that's stopped in the right lane. IMO it's fair to infer that minute for minute standing on the side of the road behind a garbage truck with orange lights moving a trash bin is more dangerous than standing on the side of the road in front of a cruiser with blue lights harassing a motorist.
If you start moving garbage cans around at age 20 in a brand new truck there's a pretty fair chance you'll be looking to switch careers at about the same time they retire that truck. If you manhandle garbage cans around every day from 5-2 your body isn't going to last.
Teachers (along with police, fire and other municipal employees) are usually paid very well for the qualifications their work requires the time they put in and the wear on their bodies. Since most teaching positions are union jobs they're incredibly stable.
Personal anecdote: the teachers I've known all seem to be on the same career path. The start working in less wealth areas and slowly move upward until they land a well paying job that they like and has a pension plan. On the way up to that job they build their resumes, libraries of lesson plans and gain experience. IMO this makes sense, the schools with the most money to throw at teachers can be picky in hiring teachers and more effective at retaining them.
If it's just a "good teacher" or two in an institution that doesn't have that ethic, using more advanced students to help less advanced ones can exploit both groups.
Now, many public school teachers have to practice "guerrilla excellence" so it's a complex problem. But a kiddo who gets algebra doesn't necessarily get teaching it.
Luckily for me I had a great teacher who recognized my boredom and stuck me in a corner with some advanced algebra and trig books and told me to get to work. Much better for me and the other students.
My oldest child is still a year away from kindergarten and from the conversations I have had with elementary school administrators it sounds like they don't really have any formal plan to handle kids that are more advanced in certain subjects. They definitely don't use the terms "talented" or "gifted" anymore. Not sure if my child would be qualified for a program like that in the future but it would be good to know that it was be available.
I was a casualty of one such experiment in Fairfax County, VA. My year, and my year only, instead of offering the usual 7th grade honors "pre-Algebra" course, they mixed the honors students with lower achieving students. It was an unmitigated disaster for those of on the honors end of the spectrum. When we entered Algebra in 8th grade, we were all well behind the expected knowledge level. I feel like it hurt me the rest of the way through high school.
As far as I can tell (from loads in internet research), Algebra-For-All and similar mixed courses have benefits for the average and below-average students, but the price is stunting the development of advanced learners.
When I learned algebra it was taught in the 8th grade or 7th grade AP. My younger sibling (only a decade apart) was learning it in the 6th grade while not placed in an advanced class. It will vary by state and school district, I imagine. It also appears to me that Preschool is less and less "optional" and more and more "required" with many expectations for Kindergarten students to know things that would have been taught to students who attended Preschool, so students who did not attend Preschool are already behind their peers before even entering the 1st grade...
Here in lies the fundamental issue of the (well intentioned) focus on No Child Left Behind. The schools tend to underserve the best students because energy is focused on the weakest. (If the weakest were being well served, this would be a worthy trade. My experience in large cities is this is the exception rather than the rule.)
This used to bother me quite a bit, but I think the best students can find other ways to be intellectually stimulated. (Online, etc) The downside is for most of school they're bored out of their mind, and this can develop bad habits for when school eventually catches up to their abilities.
My wife & I are taking the approach that responsibility for primary education lies with parents first, then teachers, so, to your first point, we don't particularly perceive this as a huge personal problem.... The fact is, education in America is classist and the kids of white collars households have incredibly unfair advantages. Bootstrapping from poverty & ignorance to professional success and higher education is harder than it's ever been.
I hear you on parental ownership. Even in the most elite NYC private schools, parents pay for tutoring or scramble to cover what they perceive to be gaps. For public schools, it's the same. A school may be good at Math, but weak at music, or vice versa. It's up to the parents to close the gaps. (And parents know their kids best)
An inverted anecdote re your statement on the the parents first point: I went to a "big east coast city public highschool". While you say that you don't see the lower effort on the top demographic as a (to your credit, personal, so I may be misinterpreting it as a generalization) problem, I'd make some following statements.
Of the people in my AP/accelerated classes, about half were _definitely_ not white collar. Parents in manual labor working 2 jobs, non-english-speaking immigrant families, etc. If we did not have what little acceleration was given, they would _never_ have gotten ANY attention they needed because their parents simply did not have it in them. It can be said that "that's their job" but even decades later I can't find any fault to their focus on providing some vestige of financial stability first.
What I'm saying is that by assuming all families CAN have the parents shoulder education is an assumption rooted in much more of what I've seen of white collar than blue collar families. Pushing all families to take this on would likely hurt those without the spare time and background far more than those with. ANY opportunities we provide in that sense will continue to cyclically reinforce those with the resources to better leverage future opportunities. While I am not disagreeing to how invaluable teaching at the home is, I see publically taxed schooling as the great leveler, where the people have the chance to reallocate some of this opportunity to where it is most effective.
Now, for the "incendiary" part of this post; where is "most effective", while I'm no teacher I can also say that a one size fits all policy with only the option of "do this material more deeply" for extention would absolutely _gut_ what little educational value existed for some of the top tier students in a comparable fashion to if you pushed the remedial classes into middle school calc. If I've learned one thing from decades in school, (and as an interesting tidbit, supplemented by years of open offices) it's that humans are so hilariously far from "one size fits all" in how they learn, and while reasonably consistent in "you'll get to do less of this near-purgatory experience" being FAR more of a motivator than "you'll get to do more", it's individualization and communication that bridges this gap, not regimentation.
Regardless, those kids who went straight to college from middle school seemed 10x better off and all of the ones I know (or am friends with) are doing great.
We used the Saxon math program when I was in elementary/middle school, and the repetition was key there. I could get away with teaching myself, because I'd be seeing the same classes of problems over, and over, and over, long after I finished up the chapter introducing them. Unfortunately, after 7th grade, and burning through the Algebra 1 book, the district switched curriculums, and I didn't learn anything new until I took discrete math in college.
As for the "social aspect", you rarely actually get to work with peers, and instead are coerced into doing the teacher's job for them. It was incredibly frustrating to drag along with people who just didn't have the brainpower to deal with the material.
Might be worth considering the effects of changing teacher demographics. For a variety of reasons the public employee unions have been eliminated, and a side effect of that is the old salary model had very low pay for the first years of teaching (like $20K) vs very high pay after 20 years in (like $80K) averaging out to a decent living, in the end. But if higher ed profits the more teachers they produce, such that they graduate 20K for 10K of job openings or whatever, plus the teachers union is toothless if not gone, that means all the teachers at my kid's middle school are under 30 and make less than $25K/yr. And this in a "good district", in fact academic award winning (the kids culture and genetics obviously matter a lot more than teacher salaries WRT outcomes). "When I was a kid" teachers were an interesting cross section of humanity from old to young, but now 95% of them are under 30. The district likes to brag about the teachers so we get a list of diplomas from the better universities (remember higher ed graduates twice as many diplomas as there are jobs, so the only people getting jobs are above median...) the side effect is that the average BS degree in Ed at my kids school was awarded around 2010 or so. The job title of an experienced teacher is "realtor" or "waitress" or honestly I donno but I assure you there are no experienced teachers employed by school districts anymore.
So the point of this is you can't handwave away demographic change... My Algebra II teacher was maybe 50 and knew her stuff after teaching it a few decades, ditto my high school calculus teacher who must have been 60. I had a parental-age economics teacher who was very influential, ditto an influential parental age history teacher and a grandfatherly government/social studies teacher. But those days are over and the financial savings of only hiring kids to teach kids are obvious BUT its also obvious that almost nobody in the building has more than maybe 5 years experience teaching. Saving money is cool, but it results in the blind leading the blind. You NEED a curricula and overall plan that assumes all teachers are inexperienced and more or less incompetent because for financial / political reasons that's what we have today to save money.
In the DC region, I know 4-5 former teachers who moved into corporate training of one flavor or another. Usually internal positions (not consulting), so low travel, reasonably stable, with reasonably high degree of knowledge/skill transfer from teaching kids.
Bored smart kids can be just as distracting as frustrated average (and below) kids.
This is something that I noticed as a significant problem when living in the freshman dorms during undergrad. You had a lot of smart kids who spent most of the school day bored, and they spend most of the school day reading novels in class before going home to spend 40+ hours a week playing video games or browsing reddit, all while maintaining perfect grades and never having to ask for help from teachers or peers.
Then, they get to college where they encounter material that actually challenges them, but they're still in the habit of spending the hours of 3 PM to 11 PM playing World of Warcraft or League of Legends, and when they start falling behind they're still in the mindset of "I'm the smart kid, I shouldn't need to ask for help." You have kids who were high school valedictorians who end up failing classes during undergrad because they never learned how to properly function in a challenging academic environment. It can be quite a shock to transition from an environment where you might be in the 99th percentile of performers (top marks without having to try hard) to be one where you may not even be in the top 50% and actually need to put in more effort than your peers.
The primary issue imo is that math teachers do not seek to inspire students to see mathematics for what is is- a structure way to reason as opposed to a calculation tool replaced by computers. These breeds not only an aversion to the subject by fails to fulfill the basic reason for teaching math.
My best math teacher in school gave us a lecture on chaos - this was algebra class and we were able to generate a fractal by a simple set of coin tosses. This evolved into the discussion of how prbability, physics/randomness of coin tosses and the general notions of chaos and dynamical systems. But such initiative and teachers were never rewarded.
It's sad to see that the education problems seem to be regressing
The accelerated kids would essentially be forcibly held back. The curriculum at my high school for the normal accelerated student was Algebra II, Trig/Calc A (calc I), calc BC (calc II), then calc III, and we had students even more accelerated than this. Starting at Algebra I in high school, would essentially shift everything back two years.
tl;dr Why Did San Francisco Schools Stop Teaching Algebra in Middle School? They didn't. The topics of algebra are now spread through the middle school courses along with other foundations of geometry and probability/statistics. However, they did restructure the names and pathways in high school in such a way that might impact the way ability of a student to take a 2nd course in Calculus by Senior year of high school.
Because the school superintendent and the board of education believe much more strongly in wealth redistribution and social equality than many of the constituents do. Local elections: They matter.
Also, as the article says, the headline is clickbait. Common Core scatters algebra all over elementary school. The “traditional” curriculum, many years of arithmetic followed by Algebra I and II, geometry (plus proofs), trigonometry, and calculus, that is a harmful segmentation of math. Many students learn to hate and reject math before they even reach the parts that are useful to daily life.
The trick is getting teachers to teach the Common Core curriculum. The uncomfortable truth is that many teachers have no business teaching math, and leave students horribly confused about what math actually is. I even encountered a (SFUSD) middle school math teacher who uses jokes to try to make math fun, but his children (going to SFUSD schools) grew up hating math.
I tested out of pre algebra in 7th grade because my dad basically taught me it over the summer. Took geometry in 8th grade. Took algebra 2 at community college over summer took pre calculus my freshman year, and took ap calculus my sophomore year but halfway through the year I found it too slow so I took calc bc online with Stanford.
But then I took multivariate calc my junior year at a local cc and got a B in a math class for the first time ever. I got burnt out. And I hadn't learned the study methods required to succeed in college level mathematics. So even though I had always loved math and went into college first semester taking upper div math, I found myself disliking it more and more and eventually switching to economics. I think, had I not rushed so much, I may have have actually enjoyed it more and fully majored in it.
On the article topic, this is pretty bad. Common Core 'intuitive' BS aside, kids need earlier exposure to algebraic concepts, it was the main reason they failed the elementary calculus and probability courses in college that I ended up teaching them. It was very draining to be wasting my time trying to explain to a senior at Georgia Tech how to solve 2x=1 and then by analogy 3x=1, though they could see no similarities between the two equations.
http://www.sfusdmath.org/uploads/2/4/0/9/24098802/ccss-math-...
It says that Algebra was previously introduced in 8th grade and students were not prepared. Therefore they have moved that algebra content into normal math for grades 6-8, gradually introducing contents, along with other concepts. Then the full Common Core compliant Algebra class that focuses solely on Algebra is in 9th grade and they are hoping that students will do better with this approach.
The article and the commentary here indicate that neither the author nor any but a very small number of commenters here bothered to look at the actual program, preferring to revel in personal suppositions and speculations.
Elementary School (Primary in the UK): Kindergarten First through Sixth grades
Middle School: 7th and 8th grades
High School (Secondary in UK): 9th through 12th grade (or, freshman, sophomore, junior, and senior).
The boundary between each level varies, but I'd guess 70-80% of districts follow the above. The most common variation seems to be grouping 6th grade into middle school.
Of course, in most places private schools and even home schooling is an option, so all hope is not lost. And public education is good for many kids.
It's the one-size-fits-all approach that is not always so effective.
I know I'd have dealt with that far better than the "Do this page of 100 addition/subtraction problems as fast as you can" human calculator stupidity thrust upon us as math education. At least it sounds like common core is getting away from that sort of stuff.
Based on what I'm saw coming home from my first grader, they are. The common core stuff at least comes from people who understood that having the student do a couple thousand "1 + 2 = ____" problems tends to promote the incorrect idea that the = symbol means "do the thing on the left and write it down", and I noticed a mix of "1 + __ = 3" and "___ = 1 + 2" in the problem sets.
I noticed enough other places where the good ideas had been visibly chewed on by "the process" that I'm still not ecstatic about "common core", but at least the bits I've seen (up to first grade now) I do concede that there were good ideas at the beginning of the process. I'm not entirely convinced they made it through correctly, but they were there at the start. (Still a bit pissed that they took my kid who was adding single-digit numbers in his head and forced him to count on his fingers because That's What The Curriculum Says, though. Seems to have gotten over it by the end of the year, though, so no permanent damage. Still.)
The standards are being ruined by terrible curricula providers, to the point where people conflate the standards and the curricula.
The normal progression around here had (and I'm guessing still has) algebra starting in 8th. Kids handled it fine...I think. (Yes, some better than others of course.) So it surprises me that in SF, 8th grade was the year when the advanced class is just starting algebra and most not beginning until 9th.
Is that the norm around the country?
Read about the history (and failure) of the New Math movement. https://en.wikipedia.org/wiki/New_Math
If a kid can't do division and knows it, how can they approach a problem like, "It is 800 miles from Denver to LA by train. train A leaves from Denver to LA at 80mph while train B leaves from LA to Denver at 70mph. How far from LA do the trains cross paths?" We can start breaking this down:
70mi*x/h + 80mi*x/h = 800mi
x * 70mi/h = M
150mi*x/h = 800mi
x = 800mi/(150mi/h)
x = 5.33...h
M = 5.33h * 70mi/h
M = 373.333...mi
The problem is, a lot of kids don't get division. Why? That's above my pay grade. If I was going to take a stab in the dark, I'd say that at the highest level it's to do with passing kids who shouldn't be passing, and then teaching the next year's class as if they already know what they need to know. Every year they fall a little bit more behind, until finally they're so lost it's hopeless. It's easy to take aim at algebra but what about the shaky foundation we're trying to build it on? Of course, this would require a lot of kids to be held back, and that's not an appealing solution. I think we need to assess where in our math education kids start to fall behind, and figure out what's wrong there. Unfortunately for the kids, the solution will probably involve more multiplication/division drill sheets, and more word problems to test those skills.
The article also points out the difficulty in starting a STEM degree without calculus. I started a STEM degree without calculus. I was lucky to get into the university I got into without calculus, and the calc 1 course was taught as a remedial class for all the folks who got 4s instead of 5s on their AP calc exams. This is where I had my own first brush with trying to build the next layer of mathematics education on a shaky foundation. It was very difficult, I nearly quit, and it fucked up my GPA enough I was still paying for it four years later at my graduation. I was 18 and had a bright future to look forward to in graduating from a respected university with a STEM degree, and it was nearly too much for me. I don't see how we can ask 13 year old kids to do the same with algebra. We need to work out the kinks on the way there. When it's time for them to learn algebra we want them to have all the tools they need so they can focus on the algebra, not on the arithmetic.
To be clear, I don't have any solutions here. Just a lot of problems.
There are many reasons why students fall behind (many of which have nothing to do with school at all), but one of the reasons they _stay_ behind is failure of the educational system to focus on "THE BASICS" before moving on to more advanced topics.
The thing about mathematics education is that there are no shortcuts. Students HAVE TO understand and master previous material before moving on to the next topic.
I think it is smart the SF schools are waiting until high school to teach algebra. Most kids simply aren't ready for algebra before that time. The few that are ready can always get on an advanced track but it won't be many.
Mandated equal outcomes coupled with racial diversity.
> but ensures that all students enter high school with the same mathematical foundation
There's a saying among conservative wags: "The opposite of quality is equality."
That seems to be the case here.